Linear Programming Model

Every network flow model has a linear programming model, that is a model
with algebraic linear expressions describing the objective function and
constraints. We explain here the model for the specific case above, and
will provide in the Vocabulary Section, the general model.

For construction of the model, it is convenient to number the nodes
and arcs for reference as in Fig. 2.

Figure 2. Representation for Linear Programming Model.

The linear programming model is an algebraic description of the objective
to be minimized and the constraints to be satisfied by the variables. The
variables are the flows in each arc designated by x1 through x17. The network
flow problem is to minimize total cost while satisfying conservation of
flow at each node. The variables must also satisfy the simple upper and
lower bounds on arc flow.